Various systems are available and used to manufacture sheets of paper and other paper products. The sheets of paper being manufactured often have multiple characteristics that are monitored and controlled during the manufacturing process, such as dry weight, moisture, and caliper (thickness). The control of these or other sheet properties in a sheet-making machine is typically concerned with keeping the sheet properties as close as possible to target or desired values.
There are often two different types of actuators that are used to control the sheet properties in a sheet-making machine. First, there are machine direction (MD) actuators that typically affect only the cross direction average of a sheet property. The MD actuators often can have different dynamic responses with respect to a sheet property. Second, there are cross direction (CD) actuators that are typically arrayed across a sheet in the cross direction. Each array of CD actuators can usually affect both the average of a sheet property and the cross direction shape of the sheet property. The CD actuators often can have different dynamic responses and different spatial responses with respect to a sheet property.
The overall control of the sheet properties is often a large-scale multivariable problem. For example, one CD actuator in a CD actuator array typically affects several sheet properties in adjacent CD zones. Also, a CD actuator array intended to control a particular sheet property can often affect the average of several sheet properties, which may also be affected by several MD actuators. The overall control of the sheet properties is also often a problem of very large scale. A typical sheet-making process may have thousands of outputs (such as sheet property measurements) and hundreds of inputs (such as actuator set points). In addition, the manufacturing process can often be difficult or impossible to control in certain spatial and intra-actuator set directions.
In conventional sheet-making equipment, the control of sheet properties is often separated into two control problems. First, the CD average is controlled only utilizing the MD actuators. Second, the CD actuators arrayed across the sheet are only utilized to control the CD variation in and around the average of the sheet properties. There are also MD control schemes available that utilize model predictive control with explicit h  constraint handling for coordinating the MD actuators.